Black screen, constant vibrating plugged in?

I have had my Green iPhone 5c with AT&T since March 2014, I have taken great care of this phone, I used it regularly and dropped it maybe once or twice on carpet, nothing ever major. Top left corner of my phone popped out but it never seemed to mess with the function of my phone at all so I left it be. On September 26th of this year I was out at dinner and dropped the phone on its face and once I picked it up the screen was completely black, but lit, as if the back light of the phone was still on. I tried restarting the phone, charging it, and even calling and texting myself from my friends phone. While the phone was still showing apparent signs of life as in, vibrating, playing ringtones and sounds of screen shots and charger connections, the screen was still lit but completely black. After I could not find why my phone was messed up I let it sit and die for a few weeks. I then plugged it into my computer with the charger and it did not light up in black like it was doing before. The phone then started to vibrate, continuously every 5 seconds while plugged up. I have tried to hold the home and power buttons but that apparently only turns the phone off like I expected. I opened up iTunes and it just asks me to "respond on iPhone" and I cant obviously and the phone keeps vibrating every 5 seconds. I want to fix this phone since I have been using an old iPhone 4 for the past month and cannot take it anymore. Im hoping this is something simple and will take all the help I can get. Thank You!

P.S. I have not done ANY repairs on this phone, no screen, battery, etc. replacement. It is the original phone I purchased.